{
  "id": 617,
  "curve_key": "59698055233660549164123816588069092978240265625602048816:-473892195798964982379011575212130093240992855786001957144881574305821678130767447136",
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  "rank_lower_bound": 28,
  "torsion": [],
  "naive_height": 385.34074478664445,
  "faltings_height": 30.020782635085986,
  "conductor": "146806080754283912645946691250036103103192549129178367791442836064235384246697135528381871098086268955477892367096412508075044105849343251182540",
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    "29",
    "47",
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  "regulator": "316737507841880277238930117276571190.1630902381778265857238654370545557924185708501401405664286",
  "points": [
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      "2289682898170944279508659105175553/3916441",
      "-35684656516339736369674400231627045758554591960625/7750636739"
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      "1076978113306776751434925533",
      "-21405742632063398842822657016189959414375"
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    [
      "82106949517502108266810732921593/151321",
      "-340183276597850215616678918208494134607795644375/58863869"
    ],
    [
      "28606183441707399915811053194033/179776",
      "-1435409700349922191245604986756023977279107466025/76225024"
    ],
    [
      "566880224467943306389063583",
      "5061698736678920111317173218174477419475"
    ],
    [
      "-605882163605314342714272592",
      "32857457462047781009907284351350817118125"
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    [
      "4950161416316280396054296643607941552/4905181369",
      "-6156393350274898105036082445543059759821498015489875625/343544187540653"
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  ],
  "submitter": "Mundoamundo",
  "history": [
    {
      "kind": "primes_recorded",
      "user": "NDElkies",
      "at": "2026-09-09 03:55:54"
    }
  ],
  "commentary": "Fiber t = 11975/7157 of a rank-17 elliptic fibration of Elkies' K3 surface (arXiv:2608.25406). Found by a Mestre-Nagao sieve over t = a/b re-scored at 2^20, then an iterated 2-covering point search (fake 2-descent over 3000 cosets of the growing known lattice at level 0, minimal reduced quartic models, ratpoints). Basis LLL-reduced with respect to the canonical height. The 28 points are certified independent by the F2-rank of their images under the 2-descent map at the good primes.",
  "created_at": "2026-09-06 22:22:57",
  "updated_at": "2026-09-09 03:55:54"
}